Elizabeth Mansfield

In January 2015, I was elected to a Vice Presidency of the IMA, with responsibility for Learned Societies. This means I chair the IMA Research Committee and attend Executive Board and Council meetings, amongst other activities. I care deeply about access of girls to advanced mathematics teaching in schools, about socially aware mathematics, about funding mathematics research across the whole country, and about dealing with implicit bias.

My two former graduate students, Tania Goncalves
and Jun Zhao
pursue their careers, congratulations to them both!
Here is a great photo
of us at the FoCM '08 banquet in Hong Kong, where Jun, Tania and
Andy Wheeler presented posters.

Recent research funding :

The EPSRC grant,
"Group actions on function approximation spaces".
A description of the project is
is here.
I worked with Tristan Pryer
on this grant.

Teaching

I masterminded our MSc in Mathematics and its Applications
. Designed to be accessible, relevant, interesting and to foster creativity and communication
skills, students choose from 11 options and take 2 compulsory project modules.

This coming year, 2015-16 I am teaching on MA593/MA561 Lie groups and algebras, and
MA588, Mathematical Techniques and Differential Equations. I alternate teaching Lie groups and algebras with teaching
Mathematics and Music, which
involves Chladni patterns on drums, digital signal processing ie recording
music, and the geometry of music and music composition.

Professional Activities

I have been on the Council of the London Mathematical Society,
for two terms, from November, 2011 to November, 2015.

Editorial Advisory Boards

Research

Research Interests:
My research is the development of algorithms for Analysis,
in the context of symbolic computation and increasingly
numerical computation; recent papers
are on various forms of the discrete variational calculus and moving frames.
The mathematics that I use comes from commutative algebra, differential geometry,
variational calculus, integrable systems and geometric integration.

Earlier Research Funding
My previous EPSRC grant, "Symmetric variational
problems", which funded Tania and Jun, is now just finshed. A brief description is
here

Packages

diffgrob2 is a MAPLE package to simplify overdetermined systems of
nonlinear differential equations of polynomial type. The
algorithms are based on those by Buchberger for a Gröbner
basis of a polynomial ideal. This package is no longer being maintained
and is not at present available for public use. Packages which perform
related functions are Maple's diffalg package maintained by
Evelyne Hubert,
and the Maple
package rif which is available from
Allan Wittkopf's home
page.

The MAPLE package Indiff is now available. This is
a set of functions designed to calculate reductions and compatibility
conditions of systems of equations referred to a moving frame.
The theory is discussed in "
Algorithms for symmetric differential
systems", J. Foundations of Comp. Math.,1 (2001) 335-383.
The
Short Manual contains installation instructions for UNIX,
a guide to the procedures and three worked examples. There are
two versions of the code, a
readlib version
and a version suitable
for generic platforms
(non readlib
version, ie, maple just reads the file in whole, and you don't use the with command).
I currently have this working for Maple 9. The Maple
worksheets for the examples in the manual are for
invariant
differentation, an
over determined system, and a
classification problem.

Thesis

Since I am still receiving requests for my PhD thesis,
Differential Groebner Bases
here it is! Many thanks to
Katya Krupchyk for making this TeX version possible. Please note this is an
historical document (submitted 1991) and appears here without amendment,
with the exception that Chapter 6 is not included, since it
was published in its
entirety (A Simple Criterion for Involutivity, Journal of the London
Mathematical Society, 54, pages 323-345, 1996).
Superceded computer code is also not included.